SSC CGL 2024 Tier-I · 9 September 2024, Shift 1 · Quantitative Aptitude · Question 19 of 100

Text as printed on a candidate's response sheet for this shift; answer per SSC's tentative key as marked on that sheet. Solution last reviewed 6 September 2026.

Where this paper and its answers come from

SSC does not publish CGL question papers or a public answer key. The questions and options here are reproduced as printed on a candidate's own response sheet for this shift — the Commission's text, unchanged. Each answer is SSC's tentative key as marked on that sheet; SSC allowed challenges to it and never publishes a final key. The solutions are written by UnlockIAS.

The average marks (out of 100) of boys and girls in an examination are 75 and 80, respectively. If the average marks of all the students in that examination are 78. Find the ratio of the number of boys to the number of girls.

(a)1 : 3
(b)2 : 3
(c)1 : 2
(d)3 : 4

Answer

Why

Correct — B. Use alligation on the two group averages.

Boys average 75, girls average 80, the whole group averages 78.

Distance from the girls' mean: 80 − 78 = 2
Distance from the boys' mean: 78 − 75 = 3

The group sizes are in the ratio of the opposite distances, so boys : girls = 2 : 3.

Check by rebuilding the average with 2 boys and 3 girls:
(75 × 2 + 80 × 3)/5 = (150 + 240)/5 = 390/5 = 78 → option (b).

Why the others are wrong

(a)
1 : 3 — 1 : 3 puts the average at (75 + 240)/4 = 78.75, not 78. Loading the group with girls pulls the mean too close to 80.
(c)
1 : 2 — 1 : 2 gives (75 + 160)/3 = 235/3 = 78.33. It is in the right direction but still too far above the required 78.
(d)
3 : 4 — 3 : 4 gives (225 + 320)/7 = 545/7 ≈ 77.86, which undershoots. Too many boys drags the combined mean below 78.

Concept

The combined average of two groups sits between their two averages, and it sits closer to whichever group is larger.

Here 78 is 3 above the boys' 75 and 2 below the girls' 80. Because it leans towards 80, the girls must be the bigger group.

Alligation turns that into a ratio directly: the sizes are in the inverse ratio of the distances, so boys : girls = 2 : 3. The cross-over is the step candidates get wrong — the 2 that belongs to the boys' count is the girls' distance.

"Out of 100" in the stem only tells you the marks are already percentages. It plays no part in the calculation, which needs nothing but the three averages.

Key facts

Combined average = (sum of all marks) ÷ (total number of students)
Alligation: n1 : n2 = (A2 − Am) : (Am − A1), where Am is the combined average
The combined average always lies strictly between the two group averages
Here 78 lies 3 above 75 and 2 below 80, giving boys : girls = 2 : 3

Study next

Alligation and mixture, including three-group and repeated-replacement versionsWeighted average problems where one of the group sizes is asked forAverage change when a new member joins or leaves a group

Common traps

Writing the ratio as 3 : 2 by matching each group to its own distance instead of the opposite one
Assuming the group with the higher average is the larger one
Trying to assume actual student numbers when only a ratio is recoverable

Two group averages plus the combined average, with one quantity left blank, is the standard SSC alligation frame.

The answer is always reachable in two subtractions, so a long algebraic setup with x boys and y girls is wasted time in Tier-I.

Related PYQs

No directly related past PYQ was found.